Our approach is motivated by synthetic seismic data originating from large-scale
numerical in silico experiments based
on the 1994 magnitude \(6.7\)  earthquake in Northridge (California).
The experiments were performed by the Department of Earth and Environmental Sciences (LMU Munich, Germany) using the software SeisSol
[1]}, [2]}
and are used to assess critical geophysical parameters associated
with high ground motion in the event of an earthquake.
The simulated ground motion curves contain highly relevant phase variation due to different propagation velocities of the seismic waves and their varying distance to the hypocenter of the earthquake.
The complete data comprise 800 000 curves, each recorded over
30 seconds with a frequency of 2Hz.
Seismic activity has not subsided after 30 seconds in many cases, so the curves are mostly incomplete.
For more information on the data setting see
[3]}, [4]} and [5]}.
In order to investigate the structure of phase and amplitude variability of these highly variable and spatially indexed data,
we register them to spatially varying template functions learnt from the data and represent the registered curves in a lower-dimensional space.
Note that these data do not have a simple structure with additive Gaussian noise since absolute ground motion velocities are nonnegative and higher values entail higher variability (see Figure REF ).
